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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Periodic point free homeomorphism of $T^ 2$


Author: Michael Handel
Journal: Proc. Amer. Math. Soc. 107 (1989), 511-515
MSC: Primary 58F99; Secondary 57S17, 57S25
DOI: https://doi.org/10.1090/S0002-9939-1989-0965243-2
MathSciNet review: 965243
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Abstract: Suppose that $f:{T^2} \to {T^2}$ is an orientation preserving homeomorphism of the torus that is homotopic to the identity and that has no periodic points. We show that there is a direction $\theta$ and a number $\rho$ such that every orbit of $f$ has rotation number $\rho$ in the direction $\theta$.


References [Enhancements On Off] (What's this?)

  • John Franks, Recurrence and fixed points of surface homeomorphisms, Ergodic Theory Dynam. Systems 8$^*$ (1988), no. Charles Conley Memorial Issue, 99–107. MR 967632, DOI https://doi.org/10.1017/S0143385700009366
  • Handel, M., Zero entropy surface diffeomorphisms, preprint.
  • Michael-R. Herman, Une mĂ©thode pour minorer les exposants de Lyapounov et quelques exemples montrant le caractère local d’un thĂ©orème d’Arnol′d et de Moser sur le tore de dimension $2$, Comment. Math. Helv. 58 (1983), no. 3, 453–502 (French). MR 727713, DOI https://doi.org/10.1007/BF02564647

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Article copyright: © Copyright 1989 American Mathematical Society